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Lifting generic points
Published online by Cambridge University Press: 05 February 2024
Abstract
Let $(X,T)$ and
$(Y,S)$ be two topological dynamical systems, where
$(X,T)$ has the weak specification property. Let
$\xi $ be an invariant measure on the product system
$(X\times Y, T\times S)$ with marginals
$\mu $ on X and
$\nu $ on Y, with
$\mu $ ergodic. Let
$y\in Y$ be quasi-generic for
$\nu $. Then there exists a point
$x\in X$ generic for
$\mu $ such that the pair
$(x,y)$ is quasi-generic for
$\xi $. This is a generalization of a similar theorem by T. Kamae, in which
$(X,T)$ and
$(Y,S)$ are full shifts on finite alphabets.
- Type
- Original Article
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- Copyright
- © The Author(s), 2024. Published by Cambridge University Press
References
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